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Interpreting SPSS Output

Independent Samples t-Test for the Difference between Means

Example #1: Do states with a right-to-work law have lower union membership rate than states without a right-

to-work law?

1. HA: States with right-to-work laws have lower union membership rates than states without right-to-work

laws. (1 < 2)

2. HO: States with right-to-work laws do not have lower union membership rates than states without right-

to-work laws. (12)

3. t-test for the difference between two means

4. = 0.01; one-tailed test

5.

Group Statistics

21 13.58 3.700 .807

30 23.10 6.725 1.228

STATE HAS

RIGHT-TO-WORK

1

0

% UNION OF

EMPLOYED 1982

N Mean Std. Deviation

Std. Error

Mean

Independent Samples Test

10.036 .003 -5.880 49 .000 -9.52 1.618 -12.768 -6.263

-6.475 46.811 .000 -9.52 1.470 -12.472 -6.559

Equal variancesassumed

Equal variancesnot assumed

% UNION OFEMPLOYED 1982

F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

The 21 states with a right-to-work law (coded as 1) had an average of 13.58% of those employedbelonging to a union. In contrast, the 30 states without a right-to-work law had an average of 23.1% of

individuals employed as union members. To test for the statistical significance of this difference in

union membership between these two groups of states, an independent samples t-test is used.

The Levenes F-test for equality of variances equals 10.036 and is statistically significant at the 0.003

level. This indicates that two samples randomly drawn from populations with similar variances would

generate an F-test with a value of 10.036 only 3 times out of 1000 trials. This is far less likely than thedecision rule of alpha equal to 0.01 (1 time out of 100 trials) that is employed here. Therefore, reject the

null hypothesis that the variances of the two populations from which the samples were drawn are equal,

and report the t-test not assuming equal variances (second row).

The t-test for the difference between these two group means (not assuming equal variances) equals

-6.475 and is statistically significant at less than the 0.001 level for a two-tailed test. This is less than asignificance value of 0.01 (as indicated by alpha) that is employed here to determine statistical

significance. (The precise probability value for this value oftactually is 0.000000052058. This

indicates that two samples drawn at random from independent populations with means that are equal

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will generate a t-test for the difference between the sample means only 5.20 times out of one-hundredmillion trials. Thus, it is very unlikely that these samples were drawn from populations with equivalent

means as assumed by the null hypothesis.) However, in this instance we are employing a one-tailed

hypothesis test, so we must divide the reported probability value in the table generated by SPSS by 2.The t-test has a one-tailed probability value of less than 0.001 (its precise one-tailed probability value is

0.000000026029).

6. Test statistics falls inside critical area.

7. Decision: Reject Ho; The difference in union membership rates between states with right-to-worklaws and states without right-to-work laws is statistically significant. States with right-to-work laws

have statistically significant lower unionization rates than do states without right-to-work laws.

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Example #2: Do states with primary enforcement seat belt laws experience a different level of motor vehiclefatalities than states without primary seat belt laws?

1. HA: States with primary enforcement seat belt laws have motor vehicle fatality rates that are different

from states without primary enforcement seat belt laws. (12)

2. HO: States with primary enforcement seat belt laws have motor vehicle fatality rates that are not

different from states without primary enforcement seat belt laws. (1 = 2)

3. t-test for the difference between two means

4. = 0.05; two-tailed test

5.

The 11 states with a primary enforcement seat belt law (coded as 1) had an average of 1.77 motor

vehicle fatalities per 100 million vehicle miles traveled (VMT). In comparison, the 40 states without aprimary enforcement seat belt law had an average fatality rate of 1.74 motor vehicle fatalities per 100

million VMT. To test for the statistical significance of this difference in state fatality rate between these

two groups of states, an independent samples t-test is used.

The Levenes F-test for equality of variances equals 1.525 and has a probability value of 0.239, which isnot statistically significant at the 95% confidence level. Therefore, we fail to reject the null hypothesis

that the variances of the two populations from which the samples were drawn are equal, and report the t-

test that assumes equal variances (first row).

The independent samples t-test for the difference between these two group means (assuming equal

variances) equals 0.235 and has a probability value of 0.815. This probability value is greater than the

alpha level of 0.05 that is associated with the 95% confidence level.

6. Test statistics falls outside critical area.

7. Decision: Fail to reject Ho; There is not a statistically significant difference in the motor vehiclefatality rate between states with a primary enforcement seat belt law and states without a primaryenforcement seat belt law.